SOLUTION: Rectangular flower bed 30 yards long by 24 yards wide has a walk of uniform width around it if the area of the path is 1/4 that of the flower bad, find the width of the path
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Question 1136191: Rectangular flower bed 30 yards long by 24 yards wide has a walk of uniform width around it if the area of the path is 1/4 that of the flower bad, find the width of the path Found 2 solutions by ikleyn, ankor@dixie-net.com:Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! Rectangular flower bed 30 yards long by 24 yards wide has a walk of uniform width around it if the area of the path is 1/4 that of the flower bad, find the width of the path.
Find the area of the flower bed, 30 * 24 = 720 sq/yds
Find the area of the path, 720/4 = 180 sq/yds
Find the area of the total; flowerbed and path: 720 + 180 = 900 sq/yds
:
let x = the width of the path
the overall dimensions will be (2x+30) by ( 2x+24)
(2x+30)*(2x+24) = 900
FOIL
4x^2 + 48x + 60x + 720 = 900
4x^2 + 108x + 720 - 900 = 0
4x^2 + 108x - 180 = 0
simplify, divide by 4
x^2 + 27x - 45 = 0
Use the quadratic formula; a=1; b=27; c=-45
Do the math, I got a postive solution of
x = 1.575 yds is the width of the path
